Reference ID: MET-D192 | Process Engineering Reference Sheets Calculation Guide
Introduction & Context
The impeller-to-tank diameter ratio \( \frac{D}{T} \) is a primary geometric scaling parameter in agitated vessels.
It fixes the swept volume per revolution, governs the primary circulation loop size, and sets the energy dissipation length scale.
Correct selection ensures:
adequate bulk turnover to avoid dead zones;
power draw within motor and shaft limits;
similarity when translating pilot-plant data to full scale.
Typical applications include blending of miscible liquids, solids suspension, gas dispersion, heat transfer enhancement, and continuous-flow reactors.
Methodology & Formulas
Allowable \( \frac{D}{T} \) band
Industry practice restricts the ratio to avoid either an undersized impeller (poor pumping) or an oversized one (wall interference, high torque).
The accepted limits depend on impeller style:
Impeller style
Minimum \( \frac{D}{T} \)
Maximum \( \frac{D}{T} \)
Turbine (flat-blade, Rushton type)
0.30
0.50
Marine-type propeller
0.20
0.40
Other axial or mixed-flow devices
0.20
0.50
The target value supplied by the user is clamped inside these bounds:
\[ \left(\frac{D}{T}\right)_{\text{final}} = \max\left[ \left(\frac{D}{T}\right)_{\min},\; \min\left( \left(\frac{D}{T}\right)_{\text{user}},\; \left(\frac{D}{T}\right)_{\max} \right) \right] \]
Impeller diameter
Once the ratio is fixed, the impeller diameter is obtained directly from the tank diameter \( T \):
\[ D = \left(\frac{D}{T}\right)_{\text{final}} \cdot T \]
Reynolds number
The impeller Reynolds number quantifies the flow regime and selects the appropriate power correlation:
\[ Re = \frac{\rho N D^{2}}{\mu} \]
where
\( \rho \) fluid density (kg m-3)
\( \mu \) dynamic viscosity (Pa·s)
\( N \) rotational speed (s-1)
\( D \) impeller diameter (m)
Flow regime
Reynolds number range
Implication
Laminar (viscous dominated)
\( Re \le 300 \)
Froude effects negligible; use laminar power number curve.
Transitional
\( 300 \lt Re \lt 10\,000 \)
Neither purely viscous nor inertial; consult transitional correlations.
Fully turbulent
\( Re \ge 10\,000 \)
Inertial forces dominate; turbulent power number is constant.
For water-like fluids in a cylindrical vessel with four standard baffles, use a ratio of 0.3 to 0.4. This range balances pumping capacity and power draw while avoiding surface vortexing. Ratios below 0.25 reduce bulk turnover, and ratios above 0.5 can overload the motor and create an unstable free surface.
Keep the ratio constant only if geometric similarity is maintained. In practice, larger tanks often use a slightly smaller ratio (0.25–0.35) to stay within available motor sizes. Maintain constant tip speed or constant power per volume as the primary scale-up criterion, then adjust the ratio to meet mechanical constraints.
Yes. Axial-flow hydrofoils operate efficiently at 0.3–0.4 because they rely on bulk recirculation loops. Radial-flow flat-blade turbines are usually sized at 0.25–0.33; larger diameters increase power exponentially and do not improve circulation as effectively. Always verify with vendor power curves.
As viscosity rises above 5,000 cP or the fluid becomes shear-thinning:
Increase the ratio toward 0.4–0.5 to ensure the impeller contacts a larger fraction of the fluid.
Switch to a helical ribbon or anchor if the ratio must exceed 0.9.
Confirm adequate torque at low speed; power number increases sharply with diameter under laminar flow.
Worked Example – Checking the Impeller-to-Tank Diameter Ratio for a Turbine Agitator
A process engineer is designing a 2 m diameter storage tank that will be agitated with a 6-blade flat-blade turbine.
The goal is to confirm that the selected impeller diameter gives a D/T ratio within the recommended range of 0.3–0.5 for turbulent bulk mixing of water at 20 °C.
Knowns
Tank diameter, T = 2.0 m
Impeller diameter, d = 0.8 m
Fluid density, ρ = 1000 kg/m³
Fluid viscosity, μ = 0.001 Pa·s
Impeller speed, N = 2.0 rps
Step-by-step calculation
Compute the impeller Reynolds number to verify flow regime:
\[ Re = \frac{\rho N d^{2}}{\mu} = \frac{1000 \times 2.0 \times 0.8^{2}}{0.001} = 1.28 \times 10^{6} \]
Compare Re with the turbulent threshold:
\( Re = 1.28 \times 10^{6} \gg 10\,000 \) → flow is fully turbulent.
